First-Order Terms

Christian Sternagel, René ThiemannThe Archive of Formal Proofs,
2018.

Abstract

We formalize basic results on first-order terms, including a first-order unification algorithm, as well as well-foundedness of the subsumption order. This entry is part of the Isabelle Formalization of Rewriting IsaFoR, where first-order terms are omni-present: the unification algorithm is used to certify several confluence and termination techniques, like critical-pair computation and dependency graph approximations; and the subsumption order is a crucial ingredient for completion.